Claims & Evidence Registrar › H05
Label sentence at the locator (PDF p.175 (bytes of record)):
for every one of the 21 faithful classes, mult(8, 1) = 0 or mult(1, 3) = 0 in 56 ↓ ι = Λ2 8 ⊕ Λ2 8̄.
For every one of the 21 enumerated faithful compact su(3) ⊕ su(2) classes, the restricted 56 lacks either the colour adjoint (8,1) or the weak adjoint (1,3).
| carrier | 56 restricted through the enumerated faithful branchings of the su(8) fundamental |
|---|---|
| domain | The simultaneous-adjoint multiplicity test, not an independently certified domain-wide completeness result. |
| group | su(3) ⊕ su(2) |
| hypotheses | Use the 21 faithful classes enumerated in Appendix F §2.; The carrier restricts as Λ²8 ⊕ Λ²8̄. |
| quantifier | Every class in the printed finite census. |
| real form | Compact su(3) ⊕ su(2) inside su(8) |
Scientific status: UNDER REVIEW — the house has not adjudicated CURRENT / CONTESTED for this record (charter §10.3); a drafted claim is a claim under review, not a result.
Key — use ≠ record. A review state printed on a source use below names that use — one citation of the suite, read by the lane named in its warrant — not this record. The record's own review state is the one in the table above and is unchanged by any use-level state; a use may be LANE_PROPOSED or REVIEWED while the record it sits on remains IN_REVIEW (R45, R49).
Quotes are verbatim from the sha-pinned text extraction of the Rev33.1 PDF (A1584 §2.2, S309): mathematical typography — radicals, exponents, ≅ — can appear displaced in the extracted line. The PDF page is authoritative; the quote is what the machine gate matched.
Appendix F, §2, Proof step L4: adjoint multiplicities — PDF p.181 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS
for every one of the 21 faithful classes, mult(8, 1) = 0 or mult(1, 3) = 0 in 56 ↓ ι = Λ2 8 ⊕ Λ2 8̄.
Appendix F, §2, Proof step L4: exceptional class — PDF p.181 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS
Twenty classes have mult(8, 1) = 0; the unique (8, 1)- bearing class, 8 = (1, 2) + (3, 1) + (3̄, 1), has mult(1, 3) = 0.
| kind | reference | line / key | availability | note |
|---|---|---|---|---|
| computational | Appendix F §2, character arithmetic and equivariant-kernel census, pp.175–176; A759 | — | unknown | The source reports agreement of two census methods and a blind replication; their programs, full tables and outputs are not supplied here. |
This table covers the values this record DECLARES, not every numeral printed on this page: group labels such as E7(7), section numbers and page numbers are not declared values and are not listed here.
| value as printed | page | digit source |
|---|---|---|
21 | PDF p.175 (bytes of record) | suite text p.175 only (no kernel line found) |
3 | PDF p.175 (bytes of record) | suite text p.175 only (no kernel line found) |
2 | PDF p.175 (bytes of record) | suite text p.175 only (no kernel line found) |
56 | PDF p.175 (bytes of record) | suite text p.175 only (no kernel line found) |
8 | PDF p.175 (bytes of record) | suite text p.175 only (no kernel line found) |
1 | PDF p.175 (bytes of record) | suite text p.175 only (no kernel line found) |
| states a predicate | yes |
|---|---|
| uses on the record · unblocked | 2 · 2 |
| uses any lane has read | 2 of 2 |
| REVIEWED SUPPORTS use on the predicate, read by two non-drafting lanes | yes (2) |
| a SUPPORTS use on the predicate is DISPUTED | no |
| machine certificate current | yes |
| state | MACHINE_CHECKS_PASSED | |||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| policy | sgtoe-clearance-policy-1.0-RATIFIED · sha16 ef7d6e7690514311 | |||||||||||||||||||||
| bound to master | aad7a3ec6ce3b510 (the master the checks ran on; issued 2026-09-26T05:06Z) | |||||||||||||||||||||
| checks |
|
A certificate says the record is well-formed, current, quote-on-page, label-literal, edge-resolved and binding-consistent on the bytes it was issued on. It is not a review, and it goes STALE the moment the master moves under it (R68). It is one conjunct of the PUBLISHED condition (R67), never the whole of it.
| March library (v1) antecedents | no legacy antecedent identified |
|---|---|
| Track-2 claim ids | B-BR-01 — cross-reference; the Track 1 / Track 2 join sets each one against what the sealed suite prints for this record. Where they differ, the suite is the record. |
| serials | A759 |
| candidate ids (frozen list S304) | C2-037 |
C2-037 retains its finite-census scope. The suite prints a broader Theorem 2.1 and proof outline, but this drafting record does not certify its completeness bridges. No local theorem heading is used as a scorecard tier.
round D1253 · parsed 2026-09-06T00:06Z · machine gates passed: CONTRACT, G1-quote-on-page, G2-numerals-declared, G4-ids-resolve, DAG-acyclic · content sha256 a16cb954b5582ef38db9579c37914f1d04ba8316b11f6d31ff6d42efd7a7ba58
Reviewer verdict line (one per entry, as text): LIB2-076 | PASS or FAIL(G1–G8) or NOT RUN | quote | PDF page | one sentence. G1 source supports the exact scoped assertion · G2 evidence class fits (numbers ≡ digit source) · G3 labels as printed, not converted · G4 comparison typed · G6 public scope · G7 history real · G8 caution present and true. Machine surfaces: index.json · capsule.md.
Generated from library_v2.jsonl. Declared volatile fields (R36): BUILD_STAMP.
BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02